Method and apparatus for fabrication and tuning of grating-based differential phase contrast imaging system
A method for assembling a phase contrast x-ray imaging system includes fabricating a phase grating and an absorption grating according to a preselected pitch of the gratings. The actual obtained pitches are measured and a source grating is then fabricated according to a desired design point of the imaging system.
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This application claims priority to U.S. patent application Ser. No. 61/939,925, filed Feb. 14, 2014, in the name of Baturin et al., and entitled “METHOD AND APPARATUS FOR FABRICATION AND TUNING OF GRATING-BASED DIFFERENTIAL PHASE CONTRAST IMAGING SYSTEM.”
This application is related in certain respects to U.S. patent application Ser. No. 14/143,254, filed Dec. 30, 2013, in the name of Baturin et al., and entitled LARGE FOV PHASE CONTRAST IMAGING BASED ON DETUNED CONFIGURATION INCLUDING ACQUISITION AND RECONSTRUCTION TECHNIQUES; U.S. patent application Ser. No. 13/729,443, filed Dec. 28, 2012, in the name of Baturin et al., and entitled SPECTRAL GRATING-BASED DIFFERENTIAL PHASE CONTRAST SYSTEM FOR MEDICAL RADIOGRAPHIC IMAGING; and U.S. patent application Ser. No. 13/724,096, filed Dec. 21, 2012, in the name of Baturin et al., and entitled GRATING-BASED DIFFERENTIAL PHASE CONTRAST IMAGING SYSTEM WITH ADJUSTABLE CAPTURE TECHNIQUE FOR MEDICAL RADIOGRAPHIC IMAGING, all of which are hereby incorporated by reference as if fully set forth herein in their entirety.
BACKGROUND OF THE INVENTIONThe subject matter disclosed herein relates to differential phase contrast imaging (DPCI), in particular, to methods and apparatus for optimizing grating alignment and grating dimensions to produce maximum phase contrast.
Phase contrast imaging (PCI) has emerged over the last several years as a useful imaging technique capable of probing phase characteristics of an object as complimentary information to its conventional absorption properties. Although, to date, several PCI techniques have been explored, some effort has been made to develop a grating-based DPCI technique that enables the use of a conventional broadband X-ray source. Conventional medical X-ray imaging devices rely on material absorption properties to provide information about an object's interior structure. While good contrast between strongly (hard) and weakly (soft) attenuating materials can be achieved, soft tissue differentiation can be difficult due to low relative contrast. For example, the low-contrast soft tissue materials including, but not limited to, vessels, cartilage, lung, and breast tissue, provide poor contrast in comparison to highly attenuating bone structures. The problem with soft-tissue imaging may be addressed by interferometric X-ray imaging devices, which utilize the wave nature of X-ray radiation. In addition to conventional absorption, such devices measure the phase shift experienced by an X-ray beam traversing the imaged object. The significantly larger atomic cross section of phase shift in comparison to absorption creates the potential for better sensitivity to material differentiation.
Several PCI imaging techniques may prove useful, including an interferometer technique, a diffraction-enhanced imaging technique, and a free-space propagation technique. Various difficulties associated with these techniques, such as the requirement of a synchrotron or micro-focus X-ray source, high sensitivity to mechanical instability, and large propagation distances, impose practical limitations on the development of clinically useful systems. Grating-based systems, such as Talbot-Lau PCI, may make possible an interferometer-based PCI system using a broadband X-ray source. Such a system takes advantage of the Talbot self-imaging interferometric effect to detect local phase shifts in the imaged object. Also, the geometrical alignment of the gratings may provide another technique for PCI system optimization.
An exemplary DPCI system may be assembled as shown in
The discussion above is merely provided for general background information and is not intended to be used as an aid in determining the scope of the claimed subject matter.
BRIEF DESCRIPTION OF THE INVENTIONA Moiré fringe pattern frequency and angular orientation produced in the plane of the X-ray detector D of the DPCI system 100 is a function of the gratings' axial rotation about the axis z. Axial displacement (along the z axis) as between source-to-phase (L) and phase-to-absorption (d) gratings affects system contrast. The L−d regions of highest contrast may be implemented according to design considerations, as described herein, including effects of the X-ray spectrum on image contrast. As will be described herein below, performance of the PCI system is also highly sensitive to alignment of the gratings.
A DPCI system's geometrical dimensions may be used to estimate how the system's alignment affects a frequency of a Moiré fringe pattern and system imaging contrast. Scans and analysis may be conducted by the DPCI system 100 to identify the L−d dimensions that provide optimal contrast in captured radiographic images. The optimization process of such a DPCI system can be explained with respect to both (i) relative alignment of the gratings, and (ii) identification of the L−d magnitudes.
In one embodiment, a grating-based differential phase contrast imaging (DPCI) system provides a controllable Moiré frequency pattern. The frequency may be primarily controlled by changing dimensions of a source grating G0, for example, attaching G0s with different dimensions to a ladder 401, or gratings holder, and having them swapped by moving the ladder perpendicular to a direction of the X-ray beam 104 (
for G0 and G2 gratings, respectively. Here p1, p2, and p0 are the periods of G0, G1, and G2.
In another embodiment, a DPCI system includes swappable (or movable) G0 gratings to control Moiré frequency. A phase grating and an absorption grating are manufactured according to a desired pitch of the gratings and installed in a phase contrast imaging system. An actual pitch of the gratings are determined, followed by selecting a source grating from a plurality of source gratings secured in a gratings holder of the imaging system, and using the selected source grating for radiographic imaging by the system.
In another embodiment, an assembly method includes a defined order of system fabrication, where G1 and G2 are fabricated first, G0 desired dimensions are then determined and designed according to actual (i.e., measured) dimensions of G1 and G2. Thus, fabrication of a phase grating and an absorption grating are performed first according to a selected pitch of the gratings. The actual pitch of the fabricated phase grating and absorption grating is determined, and a desired source grating is fabricated based on the determined pitch of the phase and absorption gratings.
The summary descriptions above are not meant to describe individual separate embodiments whose elements are not interchangeable. In fact, many of the elements described as related to a particular embodiment can be used together with, and possibly interchanged with, elements of other described embodiments. Many changes and modifications may be made within the scope of the present invention without departing from the spirit thereof, and the invention includes all such modifications. The drawings below are intended to be drawn neither to any precise scale with respect to relative size, angular relationship, relative position, or timing relationship, nor to any combinational relationship with respect to interchangeability, substitution, or representation of a required implementation.
This brief description of the invention is intended only to provide a brief overview of subject matter disclosed herein according to one or more illustrative embodiments, and does not serve as a guide to interpreting the claims or to define or limit the scope of the invention, which is defined only by the appended claims. This brief description is provided to introduce an illustrative selection of concepts in a simplified form that are further described below in the detailed description. This brief description is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. The claimed subject matter is not limited to implementations that solve any or all disadvantages noted in the background.
So that the manner in which the features of the invention can be understood, a detailed description of the invention may be had by reference to certain embodiments, some of which are illustrated in the accompanying drawings. It is to be noted, however, that the drawings illustrate only certain embodiments of this invention and are therefore not to be considered limiting of its scope, for the scope of the invention encompasses other equally effective embodiments. The drawings are not necessarily to scale, emphasis generally being placed upon illustrating the features of certain embodiments of the invention. In the drawings, like numerals are used to indicate like parts throughout the various views. Thus, for further understanding of the invention, reference can be made to the following detailed description, read in connection with the drawings in which:
With reference to
The geometrical properties of a PCI system 100 may be designed to achieve maximum imaging contrast. In one embodiment, the distance L from source grating G0 to phase grating G1 and distance d between phase G1 and absorption G2 grating may be selected for optimal system contrast.
In one embodiment, the Moiré frequency may be desired to be zero or at least minimized (e.g., a tuned configuration), while in another embodiment the frequency is purposely set to be non-zero (e.g., a detuned configuration). In one embodiment, the maximum contrast of the system is observed at Moiré frequency of about 0.87 cyc/mm. When the L or d distances are altered from their optimal values in order to change the Moiré frequency (i.e., increase or decrease), the contrast of the system drops as shown in
In order to modify or adjust the frequency of the Moiré pattern, it is possible to keep L and d distances at their optimal positions (i.e., in the optimal L−d region) while only changing the gratings' dimensions (i.e., p0, p1 or p2). An analysis of the effects of changing the gratings' dimensions on frequency of the Moiré pattern shows that the G1 or G2 grating dimension change has about a 40-50 times higher sensitivity than for G0. For example, when the periods of gratings G0, G1, and G2 are about 73 μm, 4 μm, and 2 μm, respectively, the frequency of the moiré pattern, which is modulated in the plane of detector D, is around 0.87 cyc/mm. In order to tune DPCI system to zero moiré frequency it may be sufficient to change dimensions of G0 by about 7% (to approximately 78 μm), while the dimensions of G1 or G2 would have to be changed by about 0.17%. When the periods of G1 and G2 are in the order of just few micrometers the 0.17% change in dimension may be difficult to realize. In another embodiment, the period of the G0 grating may be about 73 μm, and a 7% change corresponds to 5 μm, which may be relatively easier to manufacture with high precision.
Therefore, it may be useful to follow the method shown in the flow chart of
In demonstrating the feasibility of the methods described herein, we can assume a coordinate system with the y-axis aligned with the direction of the grating bars in G2 (e.g.,
Here, fx=cos(θ)/d and fy=sin(θ)/d are the interference pattern frequencies in the x and y direction, respectively, and gx,y are the frequencies of G2. The relative tilt angle as between gratings G1 and G2 is represented by θ. The X-ray detector MTF is evaluated at a measured frequency f′=1/(T′y sin(a tan(T′x/T′y))) with periods T′x=1/(fx−gx) and T′y=1/(fy−gy). Here, I0 is the intensity of the X-ray beam incident on G1 grating, and Γ2 is the average transmission through G1 and G2. Due to the micrometer dimensions of G1 grating, the frequencies fx and gx are in the order of 500 cyc/mm and cannot be detected. Therefore, the frequency summation term in the x direction has been omitted from Eq. (1). The Moiré pattern modulated by G2 onto the detector would have frequency f′ and angle α relative to the vertical y-axis, where
α=tan−1((fy−gy)/(fx−gx)) (2)
To achieve the maximum PCI system performance, the periods of G1 and G2 are manufactured such that the interference pattern period produced by G1 at Talbot distance d matches the period of G2 (i.e., fx=gx). In such a case, perfectly aligned gratings (θ=0°) would yield a uniform image for an open-field exposure. Tilting of one of the gratings using z as the rotational (tilt) axis at an angle θ (θ≠0°) would result in horizontally oriented Moiré fringes. In practice, frequencies fx and gx might not be exactly equal (fx≠gx). In such a case, the Moiré pattern with frequency f′ and angle α between fringes and vertical axis y is expected. The Moiré patterns produced at two different tilt angles θ=0.1° and θ=0.2° are shown in
The effects illustrated in
In addition to the relative gratings' axial rotation, the axial distances L and d are important for optimization of the imaging system's contrast. To find the L−d regions of optimal contrast, a series of polychromatic X-ray exposures was conducted at different L and d distances. With each run, the contrast and frequency were measured. Next, both data sets were fit with a second-order polynomial, and the results are shown in
Geometrical alignment of the system should follow the equations:
Equation (4) specifies the position of the Talbot self-imaging (n is a Talbot order) for plane waves with wavelength λ. When diverging spherical waves are used, the optimal self-imaging position changes to dsp. Equation (6) is an alignment requirement for forming constructive interference with the period defined by Equation (7). The frequency of the modulated Moiré pattern can be calculated by Equation (8). Using Eqs. (7) and (8), it can be shown that the Moiré frequency can be written as:
f′=(2p2χ−p1)/(p1p2), (9)
where χ=L/(L+dsp). When the imaging system is designed, the period of G2 may be chosen to be equal to pint, so we can write: p*2=p1/(2χ*), whereby at (*) we denote the designed value. Substituting p2* into Equation (9), we can obtain the frequency:
f′=L/(L*p2)((dsp*+L*)/(dsp+L)−1).
If L is fixed at desired distance L*, then the Moiré frequency is:
|f′|∝Δdsp/(p2L), (10)
where Δdsp is a displacement in distance between G1 and G2 (i.e., dsp=dsp*±Δdsp). Thus, the frequency of the Moiré pattern is expected to change linearly with the change of d at fixed L. This is shown in the frequency plot of
The drop in contrast for the higher energy of the X-ray spectrum may be explained by examining phase grating G1, as shown in
This phase shift is a part of the transmission function T(x,y):
T(x,y)=eiφA(x,y) (12)
where A(x,y) is the amplitude of the absorption. The groove structure of the grating will yield different phase shifts, as shown in
amp=|eiφ
The maximum phase amplitude would occur when the phase difference of π between φ1 and φ2 is achieved. For example, if φ1=0 and φ2=π, then amp=2. This sets the optimal height of the phase grating structure to be:
When the material of the phase grating and the operational energy of the X-ray beam are chosen, size h of the grating bars is fixed. In one embodiment, if Si material is used in the PCI setup with 28 keV designed energy, for example, the height of the bars should be h=36 Åm, based on an index of refraction for silicon of 6.1×10−7, and a wavelength of 0.443 Å for the 28 keV energy level. The refraction index decrement is n=1−δ+iβ where the imaginary part β contributes to the attenuation of the amplitude and the real part δ (refraction index decrement) represents the phase shift. If the X-ray energy is different from the designed value (i.e., 28 keV), the phase shift through the Si grooves is no longer optimal. This results in loss of phase amplitude and therefore system contrast.
As described herein, the performance of a PCI system is sensitive to the relative rotational alignment of G1 and G2 gratings. The θ=0.1° relative tilt of the gratings results in a Moiré fringe pattern rotated by about 45° and approximately a 20% drop in system contrast. The contrast drop of about 50% is expected at θ=0.2°. The dependence of the Moiré fringe frequency on the tilt angle is consistent between the simulation and the experiment. The Moiré frequency is independent of the energy of the X-ray spectrum, which was shown analytically and experimentally. The L−d regions of best contrast were identified. Such regions showed a linear slope, which was consistent with the theoretical prediction.
As described herein, the relationships between an imaging system's contrast and its geometry may be used to optimize its assembly and setup. As shown herein, relative misalignment of the G1 and G2 gratings, relative to source grating G0, does not dominate the contrast of PCI system because the distance between G0 and G1 (L) is significantly larger than the distance between G1 and G2 (d). However, the contrast does exhibit more sensitivity to alignment between G1 and G2. As disclosed herein, the imaging system may suffer about a 20% contrast drop for a θ=0.1° misalignment angle, which may further drop down to 50% when the misalignment angle is doubled (θ=0.2°). Such behavior of the contrast was explained by the response of the X-ray detector to changes in the frequency of the modulated Moiré pattern caused by the relative rotations of the G1 and G2 gratings. It is disclosed herein that the angular sensitivity can be reduced if a detector with better frequency response was utilized (e.g., if a CsI scintillator is used rather than a Gd2O2S or CMOS detector). The system contrast was analyzed as a function of distances L and d and found that the contrast can reach its maximum value at the specific range of L and d distances as shown in
This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.
Claims
1. A method comprising:
- fabricating a phase grating and an absorption grating according to a preselected pitch;
- measuring an actual pitch of the fabricated phase grating and absorption grating; and
- fabricating a source grating based on the actual pitch of the fabricated phase grating and absorption grating.
2. The method of claim 1, further comprising disposing the fabricated source grating, phase grating and absorption grating in a phase contrast imaging system, wherein the phase grating and absorption grating are each disposed in one of a pair of parallel planes.
3. The method of claim 2, further comprising tilting one of the fabricated phase grating and absorption grating with respect to the other at a preselected tilt angle.
4. The method of claim 3, further comprising maintaining the phase grating and absorption grating in each of the parallel planes after the step of tilting.
5. The method of claim 2, further comprising placing an object to be imaged in the phase contrast imaging system and capturing a radiographic image of the object.
6. The method of claim 3, further comprising placing an object to be imaged in the phase contrast imaging system and capturing a radiographic image of the object.
7. The method of claim 2, wherein the step of fabricating the source grating includes selecting a dimension of the source grating according to pint=p1(p0+p2)/(2p0), wherein p0, p1, and p2 are the selected dimensions of the source, phase, and absorption grating, and wherein pint is the period of the Moire pattern.
8. A method of assembling a phase contrast imaging system, the method comprising:
- fabricating a phase grating and an absorption grating according to a preselected pitch;
- measuring an actual pitch of the fabricated phase grating and absorption grating; and
- selecting a source grating based on the actual pitch of the fabricated phase grating and absorption grating, wherein the step of selecting comprising moving one of a plurality of source gratings secured in a gratings holder of the imaging system into a path of an x-ray beam.
9. The method of claim 8, further comprising disposing the selected source grating, the fabricated phase grating and absorption grating in a phase contrast imaging system, wherein the phase grating and absorption grating are each disposed in one of a pair of parallel planes.
10. The method of claim 9, further comprising tilting one of the fabricated phase grating and absorption grating with respect to the other at a preselected tilt angle.
11. The method of claim 10, further comprising maintaining the phase grating and absorption grating in each of the parallel planes after the step of tilting.
12. The method of claim 9, further comprising placing an object to be imaged in the phase contrast imaging system and capturing a radiographic image of the object.
13. The method of claim 10, further comprising placing an object to be imaged in the phase contrast imaging system and capturing a radiographic image of the object.
14. The method of claim 8, wherein the step of selecting the source grating includes selecting a source grating from the plurality of source gratings that either:
- satisfies p0/L=p2/d, wherein p0 is the selected dimension of the source grating, L is a distance between the source grating and the phase grating in the phase contrast imaging system, p2 is the period of the absorption grating, and wherein d is a distance between the phase grating and the absorption grating in the phase contrast imaging system, or
- provides a minimum difference between p0/L and p2/d from among the plurality of source gratings.
15. The method of claim 8, wherein the step of selecting the source grating includes selecting a source grating from the plurality of source gratings that satisfies p0/L −p2/d=x wherein p0 is the selected dimension of the source grating, L is a distance between the source grating and the phase grating in the phase contrast imaging system, p2 is the period of the absorption grating, d is a distance between the phase grating and the absorption grating in the phase contrast imaging system, and wherein x is a preselected design value.
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Type: Grant
Filed: Feb 13, 2015
Date of Patent: Jul 11, 2017
Patent Publication Number: 20160038107
Assignee: Carestream Health, Inc. (Rochester, NY)
Inventors: Pavlo Baturin (Rochester, NY), Mark E. Shafer (Fairport, NY)
Primary Examiner: Courtney Thomas
Application Number: 14/621,823
International Classification: G01N 23/04 (20060101); A61B 6/00 (20060101);